Find the polynomial having roots at $- 3$ , $0$ , $2$ and $3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 2 x^{3} - 9 x^{2} + 18 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 3$	$x + 3$
$0$	$x$
$2$	$x - 2$
$3$	$x - 3$

Step 2: Multiply the factors together:

P (x) = (x + 3) \cdot x \cdot (x - 2) \cdot (x - 3) = x^{4} - 2 x^{3} - 9 x^{2} + 18 x

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Find the polynomial having roots at −3 , 0 , 2 and 3 .

The polynomial generated from the given zeros is: P(x)=x4−2x3−9x2+18x

Find the polynomial having roots at $- 3$ , $0$ , $2$ and $3$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 2 x^{3} - 9 x^{2} + 18 x$